Question

Which one of the following is not a function?

(a) {(x, y) : x, y ∈ R, x² = y}
(b) {(x, y) : x, y ∈, R, y² = x}
(c) {(x, y) : x, y ∈ R, x² = y³}
(d) {(x, y) : x, y ∈, R, y = x³}

Answer 1

(b) {(x, y) : x, y ∈, R, y² = x}

$$\begin{gathered} y^2=x\mathrm{gives}\mathrm{two}\mathrm{values}\mathrm{of}y\mathrm{for}\mathrm{a}\mathrm{value}\mathrm{of}x. \\ \mathrm{i}.\mathrm{e}.\mathrm{there}\mathrm{are}\mathrm{two}\mathrm{images}\mathrm{for}\mathrm{a}\mathrm{value}\mathrm{of}x. \\ \mathrm{For}\text{example:}(2{)}^2=4\mathrm{and}(-2{)}^2=4 \\ \mathrm{Thus},\mathrm{it}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{function}. \end{gathered}$$